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Z Test Calculator
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Z test is used to compare among two mean and check whether both samples mean differ that much that they are statistically significant.It is given by formula
$Z$ = $\frac{x - \mu}{\sigma}$
Where,

$x$ = Standardized Population Mean

$\mu$ = Population Mean

$\sigma$ = Population Standard Deviation.
Z test Calculator is a statistics tool that calculates the population mean, standard deviation and the Z score of the given sample.You just have to enter the data and the standardized random variable value x to get the Z score instantly. This calculator really makes the work easier and faster without any confusions.

## Steps for Z Test Calculator

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Step 1 :

Read the given problem and observe the no of series given n and the random variable x.Find the population mean $\mu$.

Step 2 :

Find the standard deviation for each data in the series using the formula
$\sigma$ = $\sqrt{\frac{1}{N} \Sigma_{i=1}^{N} (x_i - \mu)^2}$

Substitute the value and get the answer. Form a table out of it.

Step 3 :

To find the Z score use the formula

Z score = $\frac{x - \mu}{\sigma}$

Substitute the value in the above formula and get the answer.

## Problems Z Test Calculator

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1. ### Find the z test for the following series: 20, 30, 40, 50 for x = 35

Step 1 :

The given series is 20,30,40,50 and variable x = 35
The population mean $\mu$ = $\frac{\Sigma x_i}{n}$
= $\frac{20 + 30 + 40 + 50}{4}$
= 35

Step 2 :

The variance is
For xi = 20, $\sigma^2$ = $\sqrt{(x_i - \mu)^2}$ = (20 - 35)2 = 225
For xi = 30, $\sigma^2$ = $\sqrt{(x_i - \mu)^2}$ = (30 - 35)2 = 25

For xi = 40, $\sigma^2$ = $\sqrt{(x_i - \mu)^2}$ = (40 - 35)2 = 25

For xi = 50, $\sigma^2$ = $\sqrt{(x_i - \mu)^2}$ = (50 - 35)2 = 225

The standard deviation $\sigma$ = $\sqrt{\frac{225 + 25 + 25 + 225}{4}}$

= $\sqrt{125}$

= 11.18.

Step 3 :

Z = $\frac{x - \mu}{\sigma}$

= $\frac{35 - 35}{11.18}$

= 0

Answer  :

The population mean is 35, standard deviation $\sigma$ is 11.18 and z test is 0

2. ### Find the z test for the following series: 3,4,5,6 for x = 5

Step 1 :

The given series is 3,4,5,6 and variable x = 5

The population mean is

$\mu$ = $\frac{\Sigma x_i}{n}$
= $\frac{3 + 4 + 5 + 6}{4}$
= 4.5

Step 2 :

The variance is
For xi = 3, $\sigma^2$ = $\sqrt{(x_i - \mu)^2}$ = (3 - 4.5)2 = 2.25
For xi = 4, $\sigma^2$ = $\sqrt{(x_i - \mu)^2}$ = (4 - 4.5)2 = 0.25

For xi = 5, $\sigma^2$ = $\sqrt{(x_i - \mu)^2}$ = (5 - 4.5)2 = 0.25

For xi = 6, $\sigma^2$ = $\sqrt{(x_i - \mu)^2}$ = (6 - 4.5)2 = 2.25

The standard deviation is

$\sigma$ = $\sqrt{\frac{2.25 + 0.25 + 0.25 + 2.25}{4}}$

= $\sqrt{1.25}$

= 1.118

Step 3 :

The z test is

Z = $\frac{x - \mu}{\sigma}$

= $\frac{5 - 4.5}{1.118}$

= 0.4472

Answer  :

The population mean is $\mu$ = 4.5, standard deviation $\sigma$ is 1.224 Z test = 0.4472

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